Illumination systems for illuminating a space with a variable color are generally known. Generally, such systems comprise a plurality of light sources, each light source emitting light with a specific color, the respective colors of the different light sources being mutually different. The overall light generated by the system as a whole is then a mixture of the light emitted by the several light sources. By changing the relative intensities of the different light sources, the color of the overall light mixture can be changed.
It is noted that the light sources can be of different type, such as for instance TL lamp, halogen lamp, LED, etc. In the following, simply the word “lamp” will be used, but this is not intended to exclude LEDs.
By way of an example of a variable color illumination system, an illumination system in a theatre is mentioned. During a show, it may be desirable to change the color of the lighting. However, also in the case of homes, shops, restaurants, hotels, schools, hospitals, etc., it may be desirable to be able to change the color of the lighting. In the case of a theatre or the like, the colors are typically changed with a view to enhance dramatic effects, but in other situations it may be more desirable to have smooth and slow transitions.
As should be clear to a person skilled in the art, the color of light can be represented by coordinates of a color point in a color space. In such representation, changing a color corresponds to a displacement from one color point to another color point in the color space, or a displacement of the setting of the color point of the system. Further, a sequence of colors corresponds to a collection of color points in the color space, which collection will be indicated as a path. Dynamically changing the colors can then be indicated as “traveling” such path. More in general, dynamically changing the colors of lighting will be indicated as “navigating” through the color space.
Typically, an illumination system comprises three lamps. Usually, these lamps are close-to-red (R), close-to-green (G), close-to-blue (B), and the system is indicated as an RGB system. For each lamp, the light intensity can be represented as a number from 0 (no light) to 1 (maximum intensity). A color point can be represented by three-dimensional coordinates (ξ1, ξ2, ξ3), each coordinate in a range from 0 to 1 corresponding in a linear manner to the relative intensity of one of the lamps. The color points of the individual lamps can be represented as (1,0,0), (0,1,0), (0,0,1), respectively. These points describe a triangle in the color space. All colors within this triangle can be generated by the system.
It is desirable to have a color navigation system, allowing a user to navigate through the color space in a comfortable and intuitive way. Specifically, it is desirable that a color navigation system allows the user to take such steps in the color space such that the perceived color change is constant.
In theory, the color space can be considered as being a continuum. This will allow a user to select every possible color within the above-mentioned triangle. However, calculating the stepsize in a certain step direction such that the perceived color change has a certain value requires the use of rather powerful and costly microprocessors. Therefore, it is more advantageous for a color navigation system to have a color table, comprising predefined color points. Navigating through color space then translates to making steps from one color point in the table to the next color point in the table. Navigation can then be performed easily under the control of a simple user interface. An example of such simple user interface comprises six buttons, two buttons (step-up and step-down, respectively) for each color coordinate. Actuating one of these buttons will result in a step along the corresponding color coordinate axis, the step resulting in a predefined color perception difference.
A problem in this respect is that the RGB color space is not a linear space, so that, when taking a discrete step of a certain size along one of the color intensity coordinate axes, the amount of color change perceived by the user is not constant but depends on the actual position within the color space.
In order to solve this problem, different representations of the color space have been proposed, such as the CIELAB color space, where the independent variables are hue (H), saturation (S; in CIELAB calculated with S=Chroma/Lightness), brightness (B; in CIELAB calculated from Lightness). Because of the perceptual uniformity of Lightness (i.e. a linear change of Lightness level is also perceived as a linear change of light intensity level by the user), it is advantageous to use this parameter instead of Brightness. However, to generalize the description the parameter “Brightness” will be used in the explanation next, which values are also described with a perceptual uniform distribution (e.g. in u′V′Y space, with “Y” describing intensity, perceptual uniform Brightness distribution is logarithm(Y)). The CIELAB color space can be seen as a three-dimensional space of discrete points (3D grid). Each point in this space can be represented by coordinates m, n, p, and in each point the hue (H), saturation (S), Brightness (B) have specific values H(m,n,p), S(m,n,p), B(m,n,p), respectively. A user can take a discrete step along any of the three coordinate axes, resulting in predefined and constant changes in hue, saturation or Brightness, respectively, as long as the color is inside the outer boundary of the color space (color gamut). In principle, the variables hue, saturation and Brightness are independent from each other.
A problem is now to define a good navigation algorithm, defining navigation steps such that the perceived color change is constant, in order to build a suitable table or in order to step through an existing table. According to the CIELAB theory, when a step is made from a first color point with Chroma value C1 and hue angle h1 to a second color point with Chroma value C2 and hue angle h2, the color difference ΔE is defined asΔE=√{square root over (ΔL2+ΔC2+ΔH2)}in which ΔH is the metric Hue difference, defined as ΔH= C·Δhwith C being the average of C1 and C2 and with Δh=h2−h1.
Although the above formula is precise according to theory, it appears not to be precise in people's actual perception. Thus, there is a need for an improved color difference formula that is better adapted to personal perception.
In the article “Comparative Analysis of the Quantization of Color Spaces on the Basis of the CIELAB Color-difference Formula” in ACM transactions on Graphics, Vol. 16, nr.2, April 1997, p. 109-154, B. Hill et al describe an improved color difference formula:
      Δ    ⁢                  ⁢          E      94      ⋆        =                              (                                    Δ              ⁢                                                          ⁢                              L                ⋆                                                                    k                L                            ⁢                              S                L                                              )                2            +                        (                                    Δ              ⁢                                                          ⁢                              C                ab                ⋆                                                                    k                C                            ⁢                              S                C                                              )                2            +                        (                                    Δ              ⁢                                                          ⁢                              H                ab                ⋆                                                                    k                H                            ⁢                              S                H                                              )                2            where ΔL*, ΔC*ab, and ΔH*ab are the CIELAB 1976 color differences of lightness, chroma, and hue, respectively;where kL, kC, and kH are factors to match the perception of background conditions;and where SL, SC, and SH are linear functions of C*ab.
According to the article, standard values have been assumed as follows:kL=kC=kH=1SL=1SC=1+0.045·C*ab SH=1+0.015·C*ab 
However, experiments of the present inventor have shown that the above formula does not give satisfying results. Thus, a first objective of the present invention is to provide a color difference formula giving more satisfying results in practical experiments.
A further aspect of the problem relates to the fact that the boundary of the color space is usually not a circle but has the general shape of a triangle with curved sides. In the case of saturated LED primaries, the blue primary creates a long elongated corner in the triangle, and the RED-GREEN side is relatively short. When a user navigates along this boundary in the hue direction, taking steps such that the perceived color difference ΔE in accordance with the above-mentioned formula is maintained constant, he will find that there are far more steps in the cyan-blue-magenta region than in the red-green region. This is not an attractive situation. This situation is caused by the fact that, when navigating along the boundary of the color space, it is not possible to keep both the lightness and the chroma constant, and differences in lightness and chroma are considered to contribute to perceived color differences. When navigating close to blue, differences in chroma are relatively large so that, when the perceived color difference is maintained constant, the steps in hue are relatively small.
Thus, it is a further objective of the present invention to provide a solution for this problem as well.
More particularly, the present invention aims to provide a method for calculating color steps resulting in a good compromise between the desire to have the steps being equidistant in perceived color differences on the one hand, and the desire to have substantially comparable numbers of color steps along the boundary of the color space on the other hand.